Efficient Computation in Groups Via Compression

Abstract

We study the compressed word problem: a variant of the word problem for finitely generated groups where the input word is given by a context-free grammar that generates exactly one string. We show that finite extensions and free products preserve the complexity of the compressed word problem. Also, the compressed word problem for a graph group can be solved in polynomial time. These results allow us to obtain new upper complexity bounds for the word problem for certain automorphism groups and group extensions.KeywordsPolynomial TimeAutomorphism GroupWord ProblemPolynomial Time AlgorithmFree ProductThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.